Question

If a/4 = 9/a, then

a. a2=36
b. 4a = 9a
c. a + 4 = 9 + a
d. a - 4 = 9 - a

Answer 1

Part I: Evaluating the value of "a"

Given equation:

`\cfrac{a}{4} = \cfrac{9}{a}`

To simplify the equation, we need to use cross multiplication.

`\text{Cross multiplication:}\ \huge\text{[(}(a)/(b) = (c)/(d) \huge\text{)} \implies \huge\text{(}a * d = b * c\huge\text{)} \implies ad = bd \text{]}`

After using cross multiplication, we obtain;

`\implies a * a= 9 * 4`

`\implies a^(2) =36`

Taking a square root on both sides of the equation:

`\implies \sqrt{a^(2)} =√(36)`

`\implies a =6`

Part II: Determining the correct option:

This can be done by substituting the value of "a" in all the options. The option, which is true, is correct.

Verifying Option A:

Given equation:

• a² = 36

Substitute the value of "a" into the equation

• ⇒ a² = 36
• ⇒ (6)² = 36

Simplify the left-hand-side of the equation:

• ⇒ (6)² = 36
• ⇒ (6)(6) = 36
• ⇒ 36 = 36 (True)

Verifying Option B:

Given equation:

• 4a = 9a

Substitute the value of "a" into the equation

• ⇒ 4a = 9a
• ⇒ 4(6) = 9(6)

Simplify both sides of the equation:

• ⇒ 4(6) = 9(6)
• ⇒ 24 = 54 (False)

Verifying Option C:

Given equation:

• a + 4 = 9 + a

Substitute the value of "a" into the equation

• ⇒ a + 4 = 9 + a
• ⇒ (6) + 4 = 9 + (6)

Simplify both sides of the equation:

• ⇒ (6) + 4 = 9 + (6)
• ⇒ 10 = 15 (False)

Verifying Option D:

Given equation:

• a - 4 = 9 - a

Substitute the value of "a" into the equation:

• ⇒ a - 4 = 9 - a
• ⇒ (6) - 4 = 9 - (6)

Simplify both sides of the equation:

• ⇒ (6) - 4 = 9 - (6)
• ⇒ 2 = 3 (False)

Therefore, Option A is correct.

Answer 2

Answer: Option a.

Explanation:

It is important to remember the "Product of powers property", which states that:

`(a^m)(a^n)=a^((m+n))`

Then, given the expression
`(a)/(4)=(9)/(a)`, you need to apply the Multiplication property of equality, which states that:

`if\ a=b,\ then\ a*c=b*c`

Therefore:

- Multiply both sides of the equation by "a":

`(a)((a)/(4))=(9)/(a)(a)\\\\(a^2)/(4)=9`

- Multiply both sides of the equation by "4". Then you get:

`(4)((a^2)/(4))=(9)(4)\\\\a^2=36`

This matches with the option a.